Question

I need help with this review. How do I know the right triangles are similar? And what is the ratio that is equivalent to z/x also which ratios of the side lengths are equal to tan (a)? Why are the values of the trigonometric ratios only dependent on the angle and not the particular lengths on the triangles? & the last question I have is if y/z = 0.7 what is the measure of the nearest degree?

Answer 1

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other. We have two right angles, which are equal to each other. The top angles are equal to each other, so the triangles are similar

z/x = s/q Side z is similar to s and x is similar to q

tan a = opp/ adj = y/x = r/q

The values of the trig ratios are dependent on the ratios, not the side lengths, so when the lengths change, the ratios stay the same

y/z = .7

y/z This is opp/ hyp which is cos

cos a = y/z = /7

Taking the inverse cos of each side

cos^-1 ( cos a) = cos^-1( .7)

a = 45.57

To the nearest degree is 46